Chapter 11.2, Problem 24IP

To determine

To find: Measures of the angles.

Answer to Problem 24IP

Measures of the angles are ${36}^0,{117}^0$ and ${27}^0$

Explanation of Solution

Given information:

Angles of a triangle are $4x^0,13x^0$ and $3x^0$

Given

Angles of a triangle are $4x^0,13x^0$ and $3x^0$

We know sum of angles of a triangle is ${180}^0$

Using that

We get

  $4x^0+13x^0+3x^0={180}^0$

On solving

  $\begin{array}{l}4x^0+13x^0+3x^0={180}^0\\ \Rightarrow 20x^0={180}^0\\ \Rightarrow x^0=\frac{{180}^0}{20}\\ \Rightarrow x^0=9^0\end{array}$

Therefore,

  $x=9^0$

One angle is $4x=4\left(9^0\right)={36}^0$

Second angle is $13x^0=13\left(9^0\right)={117}^0$

Third angle is $3x^0=3\left(9^0\right)={27}^0$

Therefore,

Measures of the angles are ${36}^0,{117}^0$ and ${27}^0$